MDS codes, which are codes meeting the Singleton bound, are very useful in different applications of coding theory and cryptography, such as error-correcting codes [1]}, secret sharing [2]}, and distributed storage [3]}.
The classical examples are the Reed-Solomon codes.
They are constructed as follows.
Take a finite field \(\mathbb {F}_q\)  and denote its elements as \(\alpha _1, \dots , \alpha _q\) .
Choose an integer \(k\le q\)  and for any polynomial
\(f(X) = \sum _{i=0}^{k-1} f_i X^i \in \mathbb {F}_q[X] \) 
of degree smaller than \(k\) , define \(f(\infty ) = f_{k-1}\) .
Then
\( \left\lbrace  (f(\alpha _1), \dots , f(\alpha _q),f(\infty )) \, \, || \, \, f \in \mathbb {F}_q[X], \, \deg (f) < k \right\rbrace  \) 
